A Comparison of False Positive Rates of Peto and Poly-3 Methods for Long-Term Carcinogenicity Data Analysis Using Multiple Comparison Adjustment Method Suggested by Lin and Rahman

Abstract

Statistical analyses of two-year carcinogenicity data include tests for dose-response relationship (positive trend) among the increasing doses and pairwise comparisons of treated groups with control in tumor incidence by organ/tumor combination. There are two major concerns in analyzing carcinogenicity data, namely, adjustment for the difference in mortality due to drug toxicity and adjustment for the multiplicity due to multiple testing of trends and pairwise differences by organ tumor combination. A widely used method for testing dose-response relationship is the method suggested by Peto et al. (Peto test). The Peto test adjusts the mortality differences among treatment groups by partitioning the entire study period into several intervals, analyzing the data separately for each interval, and then combining them using the Mantel-Haenszel procedure. The denominator for the calculation of the proportion of tumor bearing animals is determined from the cause of death information tumor data. In later works, researchers have expressed concerns regarding the construction of suitable intervals for mortality adjustment. Also according to the opinion of many pathologists it is difficult to accurately specify retrospectively if a tumor is the real cause of death of an animal. This information may be imprecise. Hence, many times results of analysis using the Peto test are questioned due to the inaccurate cause of death information. An alternative to the Peto test was suggested by Bailer and Portier, popularly known as Poly-K test. Unlike the Peto test, this test does not need any arbitrary partitioning of the study period or the cause of death information. This test for trend in tumor incidence adjusts the differences in mortality among treatment groups by assigning a weight of less than one to an animal that died early without developing the tumor; and a weight of one to an animal that died with the tumor or survived to the end of the study. The sum of the assigned weights of animals in a treatment group is then used as the denominator for the calculation of proportion of tumor-bearing animals for the group. The less-than-one weight assigned to an animal is the fraction of the animal's surviving time in the study over the maximum time of the study with a power k. The power k of the fraction is determined by the distribution of tumor onset times of the tumor. The Poly-K test may have some advantages over the Peto test in the sense that it does not require the cause of death information, which is an essential part for the Peto test. However, the performance of the Poly-K test in controlling the false positive rate in comparison to the Peto test is unknown and of great interest in the regulatory environment. In this work the authors compared the overall false positive rates of the Peto and Poly-K tests using the Lin-Rahman multiple comparison adjustment based on some simulation results.

Key Words:

• Carcinogenicity
• Dose response
• False positive rate
• Peto test
• Poly-K test

ACKNOWLEDGMENTS

The authors are grateful to Dr. Huque, Director Division of Biometrics-3, FDA, for his inspirations and comments on this work.

Disclaimer: The views expressed in this work are those of the authors and not necessarily of the U.S. Food and Drug Administration.

Notes

Time to tumor onset (T ₀) corresponding to each model for time to death